Field of the Invention
The present invention relates to a determination method of determining a prediction formula for predicting a fluctuation in optical characteristics of a projection optical system, an exposure apparatus, a storage medium, and a method of manufacturing an article.
Description of the Related Art
As one of apparatuses used in the manufacturing step (lithography step) of semiconductor devices and the like, there is an exposure apparatus which exposes a substrate via a projection optical system and transfers a pattern of an original to a shot region on the substrate. In such an exposure apparatus, a part of exposure light is absorbed in the projection optical system, and thus optical characteristics of the projection optical system may fluctuate under the influence of heat generated by the absorption. As a result, it may become difficult to transfer the pattern of the original to the shot region accurately.
Japanese Patent Laid-Open No. 2001-160533 proposes a method of predicting a fluctuation in optical characteristics of a projection optical system by using a prediction formula having an exposure amount, an exposure period (exposure time), and the like as variables and controlling the optical characteristics of the projection optical system based on a predicted value. Japanese Patent Laid-Open No. 63-58349 proposes a method of determining a prediction formula based on a result obtained by actually measuring a fluctuation in optical characteristics of a projection optical system so as to reduce errors generated in a predicted value.
In the projection optical system, a tendency of the fluctuation in the optical characteristics may change for each exposure condition for exposing the substrate. Therefore, the prediction formula may be determined for each exposure condition. However, actually measuring the fluctuation in the optical characteristics as described in Japanese Patent Laid-Open No. 63-58349 each time the exposure condition is changed may be a cause of preventing an increase in throughput.